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- Xavier Raynaud
- 2006

We show that the Camassaâ€“Holm equation ut âˆ’uxxt +3uux âˆ’2uxuxx âˆ’uuxxx = 0 possesses a global continuous semigroup of weak conservative solutions for initial data u|t=0 in H1. The result is obtained byâ€¦ (More)

The Camassaâ€“Holm equation utâˆ’uxxt +3uuxâˆ’2uxuxxâˆ’uuxxx = 0 enjoys special solutions of the form u(x, t) = Pn i=1 pi(t)e âˆ’|xâˆ’qi(t)|, denoted multipeakons, that interact in a way similar to that ofâ€¦ (More)

- Helge Holden, Xavier Raynaud
- SIAM J. Numerical Analysis
- 2006

We prove that a certain finite difference scheme converges to the weak solution of the Cauchy problem on a finite interval with periodic boundary conditions for the Camassaâ€“Holm equation ut âˆ’ uxxt +â€¦ (More)

- Pascal Aubry, Pierre-Edouard Beaucamps, +17 authors Renaud Sirdey
- ICCS
- 2013

The ever-growing number of cores in embedded chips emphasizes more than ever the complexity inherent to parallel programming. To solve these programmability issues, there is a renewed interest in theâ€¦ (More)

Abstract. We prove existence of global and conservative solutions of the Cauchy problem for the nonlinear partial differential equation ut âˆ’ uxxt + f(u)x âˆ’ f(u)xxx + (g(u) + 1 2 f (u)(ux))x = 0 whereâ€¦ (More)

- David Cohen, Brynjulf Owren, Xavier Raynaud
- J. Comput. Physics
- 2008

The Camassaâ€“Holm equation is rich in geometric structures, it is completely integrable, bi-Hamiltonian, and it represents geodesics for a certain metric in the group of diffeomorphism. Here two newâ€¦ (More)

Based on estimates for the KdV equation in analytic Gevrey classes, a spectral collocation approximation of the KdV equation is proved to converge exponentially fast. Mathematics Subjectâ€¦ (More)

We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation utt âˆ’ c(u)(c(u)ux)x = 0. We allow for initial data u|t=0 and ut|t=0 that containâ€¦ (More)

- KATRIN GRUNERT, Helge Holden, Xavier Raynaud
- 2010

We study stability of conservative solutions of the Cauchy problem for the periodic Camassaâ€“Holm equation utâˆ’uxxt +3uuxâˆ’2uxuxxâˆ’uuxxx = 0 with initial data u0. In particular, we derive a new Lipschitzâ€¦ (More)

Abstract. We show that the periodic Camassaâ€“Holm equation ut âˆ’ uxxt + 3uux âˆ’ 2uxuxx âˆ’ uuxxx = 0 possesses a global continuous semigroup of weak conservative solutions for initial data u|t=0 in H per.â€¦ (More)